by 1942, noun ("a cowardly escape, an evasion") and verb ("sneak off, escape, give up without trying"), American English slang, perhaps from cop a plea (c. 1925) "plead guilty to lesser charges," which is probably from northern British slang cop "to catch" (a scolding, etc.); as in cop a feel "grope someone" (1930s); see cop (v.). Sense of "evade an issue or problem" is from 1960s.
"deception, escape by artifice or deceit," 1540s, noun of action from elude, or from Medieval Latin elusionem (nominative elusio), noun of action from past-participle stem of Latin eludere.
early 15c., evasioun, "a way out, expedient," from Old French évasion and directly from Late Latin evasionem (nominative evasio) "a going out," noun of action from past-participle stem of Latin evadere "to escape" (see evade).